The constraint ability of Hubble parameter by gravitational wave standard sirens on cosmological parameters

Abstract In this paper, we present the application of a new method measuring Hubble parameter H(z) by using the anisotropy of luminosity distance ($$d_{L}$$ dL ) of the gravitational wave (GW) standard sirens of neutron star (NS) binary system. The method has never been put into practice so far due to the lack of the ability of detecting GW. However, LIGO’s success in detecting GW of black hole (BH) binary system merger announced the potential possibility of this new method. We apply this method to several GW detecting projects, including Advanced LIGO (aLIGO), Einstein Telescope (ET) and DECIGO, and evaluate its constraint ability on cosmological parameters of H(z). It turns out that the H(z) by aLIGO and ET is of bad accuracy, while the H(z) by DECIGO shows a good one. We simulate H(z) data at every 0.1 redshift span using the error information of H(z) by DECIGO, and put the mock data into the forecasting of cosmological parameters. Compared with the previous data and method, we get an obviously tighter constraint on cosmological parameters by mock data, and a concomitantly higher value of Figure of Merit (FoM, the reciprocal of the area enclosed by the $$2\sigma $$ 2σ confidence region). For a 3-year-observation by standard sirens of DECIGO, the FoM value is as high as 170.82. If a 10-year-observation is launched, the FoM could reach 569.42. For comparison, the FoM of 38 actual observed H(z) data (OHD) is 9.3. We also investigate the undulant universe, which shows a comparable improvement on the constraint of cosmological parameters. These improvement indicates that the new method has great potential in further cosmological constraints.